We look at the division of 517627 by 89 
We want to divide 517627 by 89.

On to step 1:
89 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 89

On to step 2:
51 divided by 89 is 0 with a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 51 and we're left with 51.
Bring next digit (7) of the dividend behind the 51 and repeat the process: 517 / 89

Moving on to step 3:
When dividing 517 by 89, we get 5 with a remainder of 72.
The next digit of our result is 5. 
Result so far: 5.0
If we subtract 445 from 517, we get 72.
Bring next digit (6) of the dividend behind the 72 and repeat the process: 726 / 89

Let's proceed to step 4:
89 can be fit into 726 8 times, resulting in a remainder of 14.
The next digit of our result is 8. 
Result so far: 58.0
Subtract 712 from 726 to get 14.
Include the next digit (2) from the dividend after 14, then repeat: 142 / 89

Let's proceed to step 5:
When dividing 142 by 89, we get 1 with a remainder of 53.
The number 1 becomes the next digit in our result. 
Result so far: 581.0
The remainder is 53 after subtracting 89 from 142.
Bring next digit (7) of the dividend behind the 53 and repeat the process: 537 / 89

Step 6:
537 divided by 89 is 6 with a remainder of 3.
Put 6 as the next digit of the answer. 
Result so far: 5816.0
Subtract 534 from 537 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 7:
89 goes into 30 0 times with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 5816.0
If we take 0 away from 30, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 8:
89 can be fit into 300 3 times, resulting in a remainder of 33.
Use 3 as the next digit of our solution. 
Result so far: 5816.03
If we subtract 267 from 300, we get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Step 9:
The number 89 fits into 330 3 times, leaving a remainder of 63.
The next digit of our result is 3. 
Result so far: 5816.033
The remainder is 63 after subtracting 267 from 330.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Our division results in 5816.033 with a remaining 0.0063.